Final answer:
To find the differential of the given function, take the partial derivative of z with respect to x and multiply it by dx, and then take the partial derivative of z with respect to t and multiply it by dt.
Step-by-step explanation:
The given function is z = e-4xcos(4πt).
To find the differential of the function dz, we need to take the partial derivative of z with respect to x and multiply it by dx, and then take the partial derivative of z with respect to t and multiply it by dt.
The partial derivative of z with respect to x is -4e-4xcos(4πt), so the first term in the differential is -4e-4xcos(4πt)dx.
The partial derivative of z with respect to t is -4πe-4xsin(4πt), so the second term in the differential is -4πe-4xsin(4πt)dt.